Deterministic and stochastic models for complex cardiovascular phenomena

Thursday, June 17 at 11:30am (PDT)
Thursday, June 17 at 07:30pm (BST)
Friday, June 18 03:30am (KST)

SMB2021 SMB2021 Follow Wednesday (Thursday) during the "MS20" time block.
Note: this minisymposia has multiple sessions. The second session is MS14-MMPB (click here).

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Martina Bukac (University of Notre Dame, United States), Daniele Schiavazzi (University of Notre Dame, United States)


Hemodynamic modeling has become a powerful tool in the study of basic vascular function, as well as many cardiovascular diseases. Biophysically detailed vascular simulations can reveal underlying mechanisms that help explain experimental and clinical observations. As a result, there is an increasing demand for fast and efficient numerical algorithms to solve coupled multi-physics problems arising from biomedical applications. Examples include fluid-structure interaction models (e.g., valvular modeling), fluid-porous or poroelastic medium interaction models (e.g., biological tissue or tumor modeling), as well as models of transport phenomena (e.g., transport of drugs or chemicals). Moreover, creation of realistic models might be difficult in situations where only partial knowledge is available for the input processes. Examples include, but are not limited to, uncertainty in the model anatomy, physiologic boundary conditions and material properties of the cardiac and vascular tissue. In such cases, uncertainty quantification becomes an integral part of the modeling exercise. While significant progress have been achieved in recent years, hemodynamic modeling still poses significant challenges in the mathematical and computational sciences. Thus, substantial effort is allocated to the design of adaptable and uncertainty-aware numerical methods for coupled problems due to their intricate multi-physics nature, possible strong nonlinearity and presence of uncertainty. Hence, this minisymposium focuses on methodological developments and analysis of results from deterministic and stochastic cardiovascular models.

Mitchel Colebank

(North Carolina State University, United States)
"Modeling and simulation of fluid dynamics in chronic thromboembolic pulmonary hypertension"
A compromised pulmonary vasculature can lead to pulmonary hypertension (PH), defined by a mean pulmonary arterial blood pressure (mPAP) exceeding 20 mmHg. Though there have been advances in PH treatments, only chronic thromboembolic pulmonary hypertension (CTEPH) is considered curable. CTEPH is characterized by multiple recurrent or unresolved pulmonary emboli that impede flow to the alveoli. The disease causes perfusion defects, causing small vessel disease in both obstructed and unobstructed territories. Those with lesions in the smaller arteries are treated by balloon pulmonary angioplasty (BPA), though treatment planning is clinic dependent. To address this, we propose a multiscale model of CTEPH hemodynamics that couples a one-dimensional computational fluid dynamics model (1D CFD) of the large arteries to a linearized CFD model of the small arteries and arterioles. The former is conducted in an image based geometry, while the latter fluid dynamics are simulated in a fractal, structured tree. We also integrate two pressure-loss models, mimicking typical CTEPH lesions. Our results show that the model framework predicts common phenotypes of CTEPH, including perfusion deficits, small vessel flow imbalances, and elevated mPAP. Lastly, we use the 1D model to predict hemodynamic improvements after virtual BPA, laying the foundation for an in-clinic treatment planning tool.

Charles Puelz

(Baylor College of Medicine and Texas Children's Hospital, United States)
"A fluid/structure interaction model of the human heart"
This talk will focus on our efforts towards building a computational model of the entire human heart, including the blood, valves, heart chambers, great vessels, and peripheral circulations. The heart tissues are assumed to be anisotropic hyperelastic materials immersed in blood, and blood itself is modeled as a viscous incompressible Newtonian fluid. The equations of motion are solved using the immersed finite element method. In this numerical approach, tissue displacements and forces are approximated on finite element meshes and blood velocities and pressures are approximated on a fixed and possibly locally refined Cartesian grid. Tissue geometries are generally imaged based, and constitutive laws for the tissues depend on fiber directions calculated using Poisson interpolation. Peripheral circulations in the form of 3-element Windkessel models provide boundary conditions for the heart model.

Jae Lee

(Johns Hopkins University, United States)
"Fluid-structure interaction models of bioprosthetic heart valves to study leaflet kinematics"
Bioprosthetic heart valves (BHVs) are commonly used in surgical and percutaneous valve replacement. The durability of percutaneous valve replacement is unknown, but surgical valves have been shown to require reintervention after 10--15 years. Further, smaller-diameter surgical BHVs generally experience higher rates of prosthesis-patient mismatch (PPM), which leads to higher rates of failure. Bioprosthetic aortic valves can flutter in systole, and fluttering is associated with fatigue and failure in flexible structures. The determinants of flutter in BHVs have not been well characterized, however, despite their potential to impact durability. We use an experimental pulse duplicator and a computational fluid-structure interaction model of this system to study the role of device geometry on BHV dynamics. The experimental system mimics physiological conditions, and the computational model enables precise control of leaflet biomechanics and flow conditions to isolate the effects of variations in BHV geometry on leaflet dynamics. We systematically characterize the impact of BHV diameter and leaflet thickness on fluttering dynamics. Ultimately, understanding the effects of device geometry on leaflet kinematics may lead to more durable valve replacements.

Zachary Sexton

(Stanford University, United States)
"Multiscale Hemodynamics of Autogenerated Cardiovascular Networks"
Recapitulating the complex topologies and flow physics of meso/microvascular circulation precedes the manufacturing of functional, biofabricated tissues. In this work we leverage stochastic constrained constructive optimization (CCO) methods to automatically vascularize proposed cardiac tissue perfusion volumes. This approach seeks to optimize vascular topologies with respect to costs functions derived from total hydraulic resistance and blood volume constrained to geometric assumptions imposed by Murray’s law. We introduce techniques to partially bind intermediate network solutions to accelerate the optimization process while improving algorithmic precision compared to recent literature. To assess hemodynamics within these networks, we utilize multiscale 0D-3D models for computational fluid dynamics simulations with prescribed pulsatile inflows. We compare time-averaged pressures and volumetric flow rates across CCO models constructed with varying power law constraints and cost function formulations. Furthermore, we predict hemodynamic metrics crucial in wall homeostasis and adaptation including time-averaged wall shear stress, oscillatory shear index, and regions of low shear to better identify viable network topologies for biofabrication. Our pipeline will serve as an end-to-end, open-source solution for autogenerating vascular networks and verifying local flow behavior in future engineered tissues.

Hosted by SMB2021 Follow
Virtual conference of the Society for Mathematical Biology, 2021.